### Abstract

Variational calculations of ground and excited bound states on atomic and molecular systems performed with basis functions that explicitly depend on the interparticle distances can generate very accurate results provided that the basis function parameters are thoroughly optimized by the minimization of the energy. In this work we have derived the algorithm for the gradient of the energy determined with respect to the nonlinear exponential parameters of explicitly correlated Gaussian functions used in calculating n -electron atomic systems with two p -electrons and (n-2) s -electrons. The atomic Hamiltonian we used was obtained by rigorously separating out the kinetic energy of the center of mass motion from the laboratory-frame Hamiltonian and explicitly depends on the finite mass of the nucleus. The advantage of having the gradient available in the variational minimization of the energy is demonstrated in the calculations of the ground and the first excited P3 state of the carbon atom. For the former the lowest energy upper bound ever obtained is reported.

Original language | English |
---|---|

Article number | 184106 |

Journal | Journal of Chemical Physics |

Volume | 132 |

Issue number | 18 |

DOIs | |

Publication status | Published - 2010 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*Journal of Chemical Physics*,

*132*(18), [184106]. https://doi.org/10.1063/1.3419931

**Analytical energy gradient in variational calculations of the two lowest P3 states of the carbon atom with explicitly correlated Gaussian basis functions.** / Sharkey, Keeper L.; Bubin, Sergiy; Adamowicz, Ludwik.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 132, no. 18, 184106. https://doi.org/10.1063/1.3419931

}

TY - JOUR

T1 - Analytical energy gradient in variational calculations of the two lowest P3 states of the carbon atom with explicitly correlated Gaussian basis functions

AU - Sharkey, Keeper L.

AU - Bubin, Sergiy

AU - Adamowicz, Ludwik

PY - 2010

Y1 - 2010

N2 - Variational calculations of ground and excited bound states on atomic and molecular systems performed with basis functions that explicitly depend on the interparticle distances can generate very accurate results provided that the basis function parameters are thoroughly optimized by the minimization of the energy. In this work we have derived the algorithm for the gradient of the energy determined with respect to the nonlinear exponential parameters of explicitly correlated Gaussian functions used in calculating n -electron atomic systems with two p -electrons and (n-2) s -electrons. The atomic Hamiltonian we used was obtained by rigorously separating out the kinetic energy of the center of mass motion from the laboratory-frame Hamiltonian and explicitly depends on the finite mass of the nucleus. The advantage of having the gradient available in the variational minimization of the energy is demonstrated in the calculations of the ground and the first excited P3 state of the carbon atom. For the former the lowest energy upper bound ever obtained is reported.

AB - Variational calculations of ground and excited bound states on atomic and molecular systems performed with basis functions that explicitly depend on the interparticle distances can generate very accurate results provided that the basis function parameters are thoroughly optimized by the minimization of the energy. In this work we have derived the algorithm for the gradient of the energy determined with respect to the nonlinear exponential parameters of explicitly correlated Gaussian functions used in calculating n -electron atomic systems with two p -electrons and (n-2) s -electrons. The atomic Hamiltonian we used was obtained by rigorously separating out the kinetic energy of the center of mass motion from the laboratory-frame Hamiltonian and explicitly depends on the finite mass of the nucleus. The advantage of having the gradient available in the variational minimization of the energy is demonstrated in the calculations of the ground and the first excited P3 state of the carbon atom. For the former the lowest energy upper bound ever obtained is reported.

UR - http://www.scopus.com/inward/record.url?scp=77952714184&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77952714184&partnerID=8YFLogxK

U2 - 10.1063/1.3419931

DO - 10.1063/1.3419931

M3 - Article

VL - 132

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 18

M1 - 184106

ER -